Find roots of polynomial $$ p(x) = x^5-x^4+19x^3+48x-48 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.7995\\[1 em]x_2 &= -0.5899+1.7891i\\[1 em]x_3 &= -0.5899-1.7891i\\[1 em]x_4 &= 0.6901+4.055i\\[1 em]x_5 &= 0.6901-4.055i \end{aligned} $$Explanation
Polynomial $ x^5-x^4+19x^3+48x-48 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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